Discrete Distributions

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Discrete Distributions

• (Lesson - 03/B)
• When Uncertainty is in Whole Numbers

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Types of Distribution

• Discrete Distributions
• Continuos Distributions

(Discrete data Data in whole numbers.)
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Discrete Distributions

• Bernoulli Distribution
• Binomial Distribution
• Poisson Distribution.

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Bernoulli Distribution

• Distribution for a random variable with
• 2 possible outcomes (success / failure)
• Constant probability of occurrence
• n
• Example Response to a telemarketing promotion.

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Binomial Distribution
Your experience tells you that one out of five
customers accepts the life insurance offer you
are making on the phone to randomly selected
people. What is the probability that 3 customers
will accept the offer in the next 10 calls? To
answer this question we need to know how to put
in use the Binomial Distribution.
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Binomial Distribution

• Could be used to model
• Response to a telemarketing effort,
• Effect of a drug on a sample of patient.
• Characteristics
• Independent Replication (n)
• 2 possible outcomes (success / failure)
• Constant probability of occurrence (p)

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Binomial Distribution (Cont.)

• Other events that could be modeled with Binomial
  distribution
• Survival of insects exposed to certain chemicals
  (after x-hours, live or death)
• Quality tests in control labs (defective non
  defective switches).
• Drill of an oil well (strike or dry well)
• Plane crashes
• Coin tosses

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Binomial Distribution (Cont.)
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Example Binomial Distribution
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Excel Binomial Distribution
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Poisson Distribution
Average number of guests arriving at the front
desk during lunch hour is 12 per hour. What is
the probability that three guests will arrive
during the lunch hour? To answer this question we
need to know how to put in use the Poisson
Distribution.
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Poisson Distribution

• Could be used to model
• number of occurrences in an interval of time,
• number of items demanded per customer.
• Characteristics
• independent and
• unlimited number of occurrences in some unite of
  measurement (mostly time)
• where average number (?) is constant.

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Poisson Distribution

• Other events that could be modeled with Poisson
  distribution
• Infant death per 1000 infants
• Incurring a rare disease per 1000 (elderly)
• Mortality rate for a disease per year
• Medical emergency call per hour
• Chuckholes on a freeway per mile

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Poisson Distribution

• Other events that could be modeled with Poisson
  distribution
• Misprints per page
• Number of accidents at intersection per month
• Number of paint chips on a automobile body
• Number of flaws in rolls of textile
• Number of bad sectors in a disc space

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Poisson Distribution

• Other events that could be modeled with Poisson
  distribution
• Machine (copy machine, computer system) breakdown
  per (month)
• Number of calls for a help desk / switchboard
  operator per (hour)
• Number of customers arriving per (hour)

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Poisson Distribution (Cont.)
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Example Poisson Distribution
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Excel Poisson Distribution
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Binomial vs. Poisson
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Next Lesson

• (Lesson - 03/C)
• Continuous Probability Distribution